Warm Up  For both right triangles, find the value of x. x x

Congruent Triangles CMIC 1

Objectives  Students will make conclusions about congruence based on observations of several triangles.  Students will be able to identify triangle congruence using the congruence theorems and postulates.  Students will use the word “congruent” to compare triangles.

Congruence  Two triangles are congruent if  all of the corresponding angles in both triangles are congruent  all the corresponding side lengths are congruent  Congruent means the same!  Symbol for congruent:

Notes  Naming triangles  Use the letters given at the corners of the triangle  Put a Δ in front of the letters  Naming Angles  Use the 3 letters given at the corners of the triangle  The letter where the angle is located should be in the middle of the 3 letters A X M

Triangle Congruence Theorems  SAS – Side Angle Side  If two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of a second triangle, then the triangles are congruent. 7 cm 13 cm 33˚ A B C S T U

Triangle Congruence Theorems  SSS – Side Side Side  If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. 9 cm7 cm 13 cm 7 cm 9 cm A B C G H I

Triangle Congruence Theorems  ASA – Angle Side Angle  If two angles and the included side of one triangle are congruent to corresponding angles and included side of a second triangle, then the triangles are congruent. 7 cm 33˚ 107˚ 7 cm A B C X Y Z

Triangle Congruence Theorems  AAS – Angle Angle Side  If two angles and a non-included side of one triangle are congruent to corresponding two angles and side of a second triangle, then the triangles are congruent. 33˚ 107˚ 9 cm A B C D E F

 The following are ways you can prove triangles are congruent:  SSS  SAS  ASA  AAS  You CANNOT prove triangles are congruent with ASS OR SSA Notes